Multi-objective economic statistical design of X-bar control chart considering Taguchi loss function

The present paper proposes a multi‐objective design approach for the c chart, considering in the optimization process of the chart parameters both the statistical and the economic objectives. In particular, the minimization of the hourly total quality related costs is the considered objective to carry out the economic goal, whereas the statistical objective is reached by the minimization the out‐of‐control average run length of the chart. A mixed integer non‐linear constrained mathematical model is formulated to solve the treated multi‐objective optimization problem, whereas the Pareto optimal frontier is described by the ε‐constraint method. In order to show the employment of the proposed approach, an illustrative example is developed and the related considerations are given. Finally, some sensitivity analysis is also performed to investigate the effects of operative and costs parameters on the chart performance. Copyright © 2013 John Wiley & Sons, Ltd.

Section: Introductionmentioning

confidence: 78%

“…The same reasons have been recently considered by Safaei et al . to develop a multi‐objective design approach for a static X‐bar control chart considering a specific shifts magnitude in the process parameter mean. The Authors develop an evolutionary algorithm, namely NSGA‐II, in order to obtain the Pareto optimal solutions.…”

Section: Introductionmentioning

confidence: 99%

A Multi‐Objective Design Approach for the c Chart Considering Taguchi Loss Function

Lupo

2013

“…So in the proposed model, the deviation from the target has costs more than that of the linear loss function. The relations (12) and (13) show the cost due to nonconformities of this type of loss function.…”

Section: Quadratic Loss Functionmentioning

confidence: 99%

“…Serel investigated the economic design of EWMA control chart considering loss function. Some researches on economic design consider special conditions; Safaei et al . examined economic design of

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chart considering two objective functions, average run length(ARL) constraints and Taguchi loss function.…”

Section: Introductionmentioning

confidence: 99%

Economic Design of Exponentially Weighted Moving Average Control Chart Based on Measurement Error Using Genetic Algorithm

Saghaei

Ghomi

Jaberi

2013

Control charts are one of the most well‐known statistical process control tools used for quick detecting changes in the process. One of their types is exponentially weighted moving average control chart. To apply them economically requires determination of corresponding parameters. Because the sampling is used to ensure process stability, the presence of measurement error in control charts seems avoidable. The presence of measurement error in control charts reduces their performance and delays quick reaction to changes. To reduce this effect, taking multiple measurements on quality characteristic of each unit is made. Previous researches do not consider the effect of measurement error on the cost function of control charts. In this paper, considering measurement error and taking multiple measurements, as well as linear and Taguchi loss functions for poor quality products, the cost function of exponentially weighted moving average control chart is modeled. For the proposed function, a numerical example is given, the average run length is computed using Markov chain method, and finally, optimal values of parameters are obtained using genetic algorithm. Finally, sensitivity analysis of parameters is performed, and the results indicate that when the slope of covariate function increases, the role of taking multiple measurement decreases, and in the case of measurement error, the optimum values of the parameters are significantly affected. Copyright © 2013 John Wiley & Sons, Ltd.

“…extended the procedure to the multivariate case. Recently, Safaei et al . studied the economic design of the

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control chart using the Taguchi quadratic loss function.…”

Section: Introductionmentioning

confidence: 99%

Control Charts monitoring Product's Loss to Society

Celano

Faraz

Saniga

2013

Taguchi introduced a new philosophy in quality control that accounts for the economic loss associated to process variation measured by deviations from the target value of a product quality characteristic. The Taguchi loss function has been considered in the design of control charts only for the computation of costs associated with nonconformities. This paper considers sample statistics based on the Taguchi loss function as a means to implement Shewhart control charts monitoring both the deviation from the target and dispersion of normally distributed quality characteristics. The aim of this proposed control chart is to perform on‐line quality control of a process by monitoring its quality loss cost performance over time. To compute the quality loss performance, we consider a nominal‐the‐best quality characteristic. The statistical performance of the proposed control charts has been evaluated and compared with that of widely used control charts. Implementing target costing philosophy by means of one of the proposed charts is also discussed. An example illustrates the Taguchi control chart in a practical implementation. Copyright © 2013 John Wiley & Sons, Ltd.